Properties

Label 429.2.n.d.157.9
Level $429$
Weight $2$
Character 429.157
Analytic conductor $3.426$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(157,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.157");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.n (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 157.9
Character \(\chi\) \(=\) 429.157
Dual form 429.2.n.d.235.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.25286 - 1.63680i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.77823 - 5.47283i) q^{4} +(2.25719 + 1.63994i) q^{5} +(2.25286 + 1.63680i) q^{6} +(-1.26682 + 3.89888i) q^{7} +(-3.23079 - 9.94334i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(2.25286 - 1.63680i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.77823 - 5.47283i) q^{4} +(2.25719 + 1.63994i) q^{5} +(2.25286 + 1.63680i) q^{6} +(-1.26682 + 3.89888i) q^{7} +(-3.23079 - 9.94334i) q^{8} +(-0.809017 + 0.587785i) q^{9} +7.76939 q^{10} +(-1.80345 - 2.78345i) q^{11} +5.75448 q^{12} +(0.809017 - 0.587785i) q^{13} +(3.52771 + 10.8572i) q^{14} +(-0.862170 + 2.65349i) q^{15} +(-14.2428 - 10.3480i) q^{16} +(0.435067 + 0.316095i) q^{17} +(-0.860515 + 2.64839i) q^{18} +(-0.145719 - 0.448476i) q^{19} +(12.9890 - 9.43703i) q^{20} -4.09953 q^{21} +(-8.61885 - 3.31883i) q^{22} -7.04636 q^{23} +(8.45831 - 6.14532i) q^{24} +(0.860404 + 2.64805i) q^{25} +(0.860515 - 2.64839i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(19.0852 + 13.8662i) q^{28} +(-0.836115 + 2.57330i) q^{29} +(2.40087 + 7.38913i) q^{30} +(-0.649155 + 0.471638i) q^{31} -28.1145 q^{32} +(2.08992 - 2.57531i) q^{33} +1.49753 q^{34} +(-9.25342 + 6.72300i) q^{35} +(1.77823 + 5.47283i) q^{36} +(-0.0991861 + 0.305263i) q^{37} +(-1.06235 - 0.771841i) q^{38} +(0.809017 + 0.587785i) q^{39} +(9.01403 - 27.7423i) q^{40} +(1.02420 + 3.15218i) q^{41} +(-9.23566 + 6.71010i) q^{42} +3.75472 q^{43} +(-18.4403 + 4.92036i) q^{44} -2.79004 q^{45} +(-15.8744 + 11.5335i) q^{46} +(-1.87974 - 5.78524i) q^{47} +(5.44027 - 16.7434i) q^{48} +(-7.93333 - 5.76390i) q^{49} +(6.27269 + 4.55738i) q^{50} +(-0.166181 + 0.511452i) q^{51} +(-1.77823 - 5.47283i) q^{52} +(10.3763 - 7.53879i) q^{53} -2.78469 q^{54} +(0.493976 - 9.24032i) q^{55} +42.8608 q^{56} +(0.381496 - 0.277173i) q^{57} +(2.32832 + 7.16582i) q^{58} +(0.00194626 - 0.00598998i) q^{59} +(12.9890 + 9.43703i) q^{60} +(7.97731 + 5.79586i) q^{61} +(-0.690477 + 2.12507i) q^{62} +(-1.26682 - 3.89888i) q^{63} +(-34.8524 + 25.3218i) q^{64} +2.79004 q^{65} +(0.493028 - 9.22259i) q^{66} -4.14523 q^{67} +(2.50358 - 1.81896i) q^{68} +(-2.17744 - 6.70148i) q^{69} +(-9.84245 + 30.2919i) q^{70} +(11.8848 + 8.63482i) q^{71} +(8.45831 + 6.14532i) q^{72} +(-4.36333 + 13.4289i) q^{73} +(0.276202 + 0.850063i) q^{74} +(-2.25257 + 1.63658i) q^{75} -2.71356 q^{76} +(13.1370 - 3.50529i) q^{77} +2.78469 q^{78} +(0.867738 - 0.630449i) q^{79} +(-15.1786 - 46.7148i) q^{80} +(0.309017 - 0.951057i) q^{81} +(7.46687 + 5.42500i) q^{82} +(-1.42551 - 1.03570i) q^{83} +(-7.28991 + 22.4360i) q^{84} +(0.463651 + 1.42697i) q^{85} +(8.45886 - 6.14572i) q^{86} -2.70572 q^{87} +(-21.8502 + 26.9250i) q^{88} +6.15187 q^{89} +(-6.28557 + 4.56673i) q^{90} +(1.26682 + 3.89888i) q^{91} +(-12.5301 + 38.5636i) q^{92} +(-0.649155 - 0.471638i) q^{93} +(-13.7041 - 9.95658i) q^{94} +(0.406561 - 1.25127i) q^{95} +(-8.68786 - 26.7385i) q^{96} +(-2.92823 + 2.12748i) q^{97} -27.3070 q^{98} +(3.09509 + 1.19182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.25286 1.63680i 1.59301 1.15739i 0.693534 0.720424i \(-0.256053\pi\)
0.899478 0.436967i \(-0.143947\pi\)
\(3\) 0.309017 + 0.951057i 0.178411 + 0.549093i
\(4\) 1.77823 5.47283i 0.889116 2.73642i
\(5\) 2.25719 + 1.63994i 1.00945 + 0.733405i 0.964093 0.265566i \(-0.0855587\pi\)
0.0453532 + 0.998971i \(0.485559\pi\)
\(6\) 2.25286 + 1.63680i 0.919726 + 0.668220i
\(7\) −1.26682 + 3.89888i −0.478815 + 1.47364i 0.361929 + 0.932206i \(0.382118\pi\)
−0.840743 + 0.541434i \(0.817882\pi\)
\(8\) −3.23079 9.94334i −1.14226 3.51550i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) 7.76939 2.45690
\(11\) −1.80345 2.78345i −0.543760 0.839241i
\(12\) 5.75448 1.66118
\(13\) 0.809017 0.587785i 0.224381 0.163022i
\(14\) 3.52771 + 10.8572i 0.942820 + 2.90170i
\(15\) −0.862170 + 2.65349i −0.222611 + 0.685127i
\(16\) −14.2428 10.3480i −3.56070 2.58700i
\(17\) 0.435067 + 0.316095i 0.105519 + 0.0766642i 0.639294 0.768963i \(-0.279227\pi\)
−0.533774 + 0.845627i \(0.679227\pi\)
\(18\) −0.860515 + 2.64839i −0.202825 + 0.624233i
\(19\) −0.145719 0.448476i −0.0334302 0.102887i 0.932949 0.360008i \(-0.117226\pi\)
−0.966379 + 0.257121i \(0.917226\pi\)
\(20\) 12.9890 9.43703i 2.90442 2.11018i
\(21\) −4.09953 −0.894591
\(22\) −8.61885 3.31883i −1.83755 0.707578i
\(23\) −7.04636 −1.46927 −0.734634 0.678464i \(-0.762646\pi\)
−0.734634 + 0.678464i \(0.762646\pi\)
\(24\) 8.45831 6.14532i 1.72655 1.25441i
\(25\) 0.860404 + 2.64805i 0.172081 + 0.529610i
\(26\) 0.860515 2.64839i 0.168761 0.519393i
\(27\) −0.809017 0.587785i −0.155695 0.113119i
\(28\) 19.0852 + 13.8662i 3.60677 + 2.62047i
\(29\) −0.836115 + 2.57330i −0.155263 + 0.477849i −0.998187 0.0601822i \(-0.980832\pi\)
0.842925 + 0.538031i \(0.180832\pi\)
\(30\) 2.40087 + 7.38913i 0.438337 + 1.34906i
\(31\) −0.649155 + 0.471638i −0.116592 + 0.0847088i −0.644553 0.764560i \(-0.722957\pi\)
0.527961 + 0.849268i \(0.322957\pi\)
\(32\) −28.1145 −4.96999
\(33\) 2.08992 2.57531i 0.363808 0.448304i
\(34\) 1.49753 0.256824
\(35\) −9.25342 + 6.72300i −1.56411 + 1.13639i
\(36\) 1.77823 + 5.47283i 0.296372 + 0.912139i
\(37\) −0.0991861 + 0.305263i −0.0163061 + 0.0501850i −0.958878 0.283817i \(-0.908399\pi\)
0.942572 + 0.334002i \(0.108399\pi\)
\(38\) −1.06235 0.771841i −0.172336 0.125209i
\(39\) 0.809017 + 0.587785i 0.129546 + 0.0941210i
\(40\) 9.01403 27.7423i 1.42524 4.38645i
\(41\) 1.02420 + 3.15218i 0.159954 + 0.492288i 0.998629 0.0523444i \(-0.0166693\pi\)
−0.838675 + 0.544632i \(0.816669\pi\)
\(42\) −9.23566 + 6.71010i −1.42509 + 1.03539i
\(43\) 3.75472 0.572590 0.286295 0.958142i \(-0.407576\pi\)
0.286295 + 0.958142i \(0.407576\pi\)
\(44\) −18.4403 + 4.92036i −2.77998 + 0.741771i
\(45\) −2.79004 −0.415915
\(46\) −15.8744 + 11.5335i −2.34056 + 1.70052i
\(47\) −1.87974 5.78524i −0.274188 0.843864i −0.989433 0.144990i \(-0.953685\pi\)
0.715245 0.698874i \(-0.246315\pi\)
\(48\) 5.44027 16.7434i 0.785235 2.41670i
\(49\) −7.93333 5.76390i −1.13333 0.823415i
\(50\) 6.27269 + 4.55738i 0.887092 + 0.644510i
\(51\) −0.166181 + 0.511452i −0.0232700 + 0.0716176i
\(52\) −1.77823 5.47283i −0.246596 0.758946i
\(53\) 10.3763 7.53879i 1.42529 1.03553i 0.434419 0.900711i \(-0.356954\pi\)
0.990870 0.134822i \(-0.0430461\pi\)
\(54\) −2.78469 −0.378948
\(55\) 0.493976 9.24032i 0.0666076 1.24596i
\(56\) 42.8608 5.72751
\(57\) 0.381496 0.277173i 0.0505304 0.0367125i
\(58\) 2.32832 + 7.16582i 0.305723 + 0.940919i
\(59\) 0.00194626 0.00598998i 0.000253382 0.000779828i −0.950930 0.309407i \(-0.899869\pi\)
0.951183 + 0.308627i \(0.0998695\pi\)
\(60\) 12.9890 + 9.43703i 1.67687 + 1.21831i
\(61\) 7.97731 + 5.79586i 1.02139 + 0.742084i 0.966567 0.256412i \(-0.0825405\pi\)
0.0548230 + 0.998496i \(0.482541\pi\)
\(62\) −0.690477 + 2.12507i −0.0876907 + 0.269884i
\(63\) −1.26682 3.89888i −0.159605 0.491213i
\(64\) −34.8524 + 25.3218i −4.35655 + 3.16522i
\(65\) 2.79004 0.346062
\(66\) 0.493028 9.22259i 0.0606875 1.13522i
\(67\) −4.14523 −0.506420 −0.253210 0.967411i \(-0.581486\pi\)
−0.253210 + 0.967411i \(0.581486\pi\)
\(68\) 2.50358 1.81896i 0.303604 0.220581i
\(69\) −2.17744 6.70148i −0.262133 0.806764i
\(70\) −9.84245 + 30.2919i −1.17640 + 3.62058i
\(71\) 11.8848 + 8.63482i 1.41047 + 1.02476i 0.993254 + 0.115955i \(0.0369930\pi\)
0.417213 + 0.908809i \(0.363007\pi\)
\(72\) 8.45831 + 6.14532i 0.996822 + 0.724233i
\(73\) −4.36333 + 13.4289i −0.510689 + 1.57174i 0.280302 + 0.959912i \(0.409565\pi\)
−0.790991 + 0.611827i \(0.790435\pi\)
\(74\) 0.276202 + 0.850063i 0.0321079 + 0.0988178i
\(75\) −2.25257 + 1.63658i −0.260104 + 0.188977i
\(76\) −2.71356 −0.311266
\(77\) 13.1370 3.50529i 1.49710 0.399465i
\(78\) 2.78469 0.315304
\(79\) 0.867738 0.630449i 0.0976282 0.0709310i −0.537900 0.843009i \(-0.680782\pi\)
0.635528 + 0.772077i \(0.280782\pi\)
\(80\) −15.1786 46.7148i −1.69701 5.22287i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 7.46687 + 5.42500i 0.824578 + 0.599091i
\(83\) −1.42551 1.03570i −0.156470 0.113682i 0.506795 0.862066i \(-0.330830\pi\)
−0.663266 + 0.748384i \(0.730830\pi\)
\(84\) −7.28991 + 22.4360i −0.795395 + 2.44797i
\(85\) 0.463651 + 1.42697i 0.0502900 + 0.154777i
\(86\) 8.45886 6.14572i 0.912142 0.662710i
\(87\) −2.70572 −0.290084
\(88\) −21.8502 + 26.9250i −2.32924 + 2.87022i
\(89\) 6.15187 0.652097 0.326049 0.945353i \(-0.394283\pi\)
0.326049 + 0.945353i \(0.394283\pi\)
\(90\) −6.28557 + 4.56673i −0.662557 + 0.481376i
\(91\) 1.26682 + 3.89888i 0.132799 + 0.408714i
\(92\) −12.5301 + 38.5636i −1.30635 + 4.02053i
\(93\) −0.649155 0.471638i −0.0673142 0.0489066i
\(94\) −13.7041 9.95658i −1.41347 1.02694i
\(95\) 0.406561 1.25127i 0.0417123 0.128377i
\(96\) −8.68786 26.7385i −0.886701 2.72899i
\(97\) −2.92823 + 2.12748i −0.297317 + 0.216013i −0.726435 0.687235i \(-0.758824\pi\)
0.429118 + 0.903248i \(0.358824\pi\)
\(98\) −27.3070 −2.75843
\(99\) 3.09509 + 1.19182i 0.311068 + 0.119782i
\(100\) 16.0223 1.60223
\(101\) 10.5617 7.67352i 1.05093 0.763544i 0.0785396 0.996911i \(-0.474974\pi\)
0.972389 + 0.233367i \(0.0749743\pi\)
\(102\) 0.462762 + 1.42423i 0.0458202 + 0.141020i
\(103\) −0.857268 + 2.63840i −0.0844691 + 0.259969i −0.984366 0.176133i \(-0.943641\pi\)
0.899897 + 0.436102i \(0.143641\pi\)
\(104\) −8.45831 6.14532i −0.829406 0.602598i
\(105\) −9.25342 6.72300i −0.903041 0.656098i
\(106\) 11.0368 33.9677i 1.07199 3.29923i
\(107\) −1.76051 5.41829i −0.170195 0.523806i 0.829187 0.558972i \(-0.188804\pi\)
−0.999381 + 0.0351657i \(0.988804\pi\)
\(108\) −4.65547 + 3.38240i −0.447973 + 0.325471i
\(109\) 0.283223 0.0271279 0.0135639 0.999908i \(-0.495682\pi\)
0.0135639 + 0.999908i \(0.495682\pi\)
\(110\) −14.0117 21.6257i −1.33596 2.06193i
\(111\) −0.320973 −0.0304654
\(112\) 58.3888 42.4219i 5.51722 4.00850i
\(113\) 0.171959 + 0.529235i 0.0161765 + 0.0497863i 0.958819 0.284018i \(-0.0916675\pi\)
−0.942642 + 0.333804i \(0.891668\pi\)
\(114\) 0.405781 1.24886i 0.0380049 0.116967i
\(115\) −15.9050 11.5556i −1.48315 1.07757i
\(116\) 12.5964 + 9.15183i 1.16955 + 0.849727i
\(117\) −0.309017 + 0.951057i −0.0285686 + 0.0879252i
\(118\) −0.00541973 0.0166802i −0.000498926 0.00153554i
\(119\) −1.78357 + 1.29584i −0.163500 + 0.118789i
\(120\) 29.1700 2.66284
\(121\) −4.49516 + 10.0396i −0.408650 + 0.912691i
\(122\) 27.4584 2.48597
\(123\) −2.68140 + 1.94815i −0.241774 + 0.175659i
\(124\) 1.42685 + 4.39140i 0.128135 + 0.394359i
\(125\) 1.91029 5.87926i 0.170861 0.525857i
\(126\) −9.23566 6.71010i −0.822778 0.597783i
\(127\) −17.4005 12.6422i −1.54404 1.12181i −0.947734 0.319061i \(-0.896633\pi\)
−0.596311 0.802754i \(-0.703367\pi\)
\(128\) −19.6952 + 60.6157i −1.74083 + 5.35772i
\(129\) 1.16027 + 3.57095i 0.102156 + 0.314405i
\(130\) 6.28557 4.56673i 0.551281 0.400529i
\(131\) 6.87944 0.601059 0.300530 0.953772i \(-0.402837\pi\)
0.300530 + 0.953772i \(0.402837\pi\)
\(132\) −10.3779 16.0173i −0.903280 1.39413i
\(133\) 1.93316 0.167626
\(134\) −9.33861 + 6.78489i −0.806733 + 0.586126i
\(135\) −0.862170 2.65349i −0.0742038 0.228376i
\(136\) 1.73743 5.34726i 0.148983 0.458523i
\(137\) −10.0232 7.28229i −0.856341 0.622168i 0.0705461 0.997509i \(-0.477526\pi\)
−0.926887 + 0.375340i \(0.877526\pi\)
\(138\) −15.8744 11.5335i −1.35132 0.981794i
\(139\) −5.40773 + 16.6433i −0.458678 + 1.41167i 0.408084 + 0.912944i \(0.366197\pi\)
−0.866762 + 0.498721i \(0.833803\pi\)
\(140\) 20.3392 + 62.5975i 1.71897 + 5.29045i
\(141\) 4.92122 3.57548i 0.414442 0.301109i
\(142\) 40.9082 3.43294
\(143\) −3.09509 1.19182i −0.258824 0.0996647i
\(144\) 17.6051 1.46709
\(145\) −6.10733 + 4.43724i −0.507186 + 0.368492i
\(146\) 12.1505 + 37.3954i 1.00558 + 3.09487i
\(147\) 3.03026 9.32619i 0.249932 0.769211i
\(148\) 1.49428 + 1.08566i 0.122829 + 0.0892406i
\(149\) 6.91960 + 5.02738i 0.566875 + 0.411859i 0.833969 0.551812i \(-0.186063\pi\)
−0.267093 + 0.963671i \(0.586063\pi\)
\(150\) −2.39595 + 7.37399i −0.195629 + 0.602084i
\(151\) 3.63922 + 11.2004i 0.296156 + 0.911473i 0.982831 + 0.184509i \(0.0590695\pi\)
−0.686675 + 0.726964i \(0.740931\pi\)
\(152\) −3.98856 + 2.89786i −0.323515 + 0.235048i
\(153\) −0.537773 −0.0434763
\(154\) 23.8583 29.3995i 1.92256 2.36908i
\(155\) −2.23873 −0.179819
\(156\) 4.65547 3.38240i 0.372736 0.270809i
\(157\) −2.87123 8.83673i −0.229149 0.705248i −0.997844 0.0656323i \(-0.979094\pi\)
0.768695 0.639616i \(-0.220906\pi\)
\(158\) 0.922975 2.84062i 0.0734279 0.225988i
\(159\) 10.3763 + 7.53879i 0.822891 + 0.597865i
\(160\) −63.4598 46.1062i −5.01694 3.64502i
\(161\) 8.92650 27.4729i 0.703506 2.16517i
\(162\) −0.860515 2.64839i −0.0676085 0.208078i
\(163\) 18.4169 13.3807i 1.44253 1.04806i 0.455019 0.890482i \(-0.349632\pi\)
0.987507 0.157575i \(-0.0503677\pi\)
\(164\) 19.0726 1.48932
\(165\) 8.94072 2.38562i 0.696034 0.185720i
\(166\) −4.90670 −0.380834
\(167\) −5.71097 + 4.14926i −0.441928 + 0.321080i −0.786401 0.617717i \(-0.788058\pi\)
0.344472 + 0.938796i \(0.388058\pi\)
\(168\) 13.2447 + 40.7630i 1.02185 + 3.14493i
\(169\) 0.309017 0.951057i 0.0237705 0.0731582i
\(170\) 3.38021 + 2.45586i 0.259250 + 0.188356i
\(171\) 0.381496 + 0.277173i 0.0291738 + 0.0211960i
\(172\) 6.67677 20.5490i 0.509099 1.56684i
\(173\) −2.46288 7.57996i −0.187249 0.576293i 0.812731 0.582639i \(-0.197980\pi\)
−0.999980 + 0.00634603i \(0.997980\pi\)
\(174\) −6.09561 + 4.42872i −0.462107 + 0.335741i
\(175\) −11.4144 −0.862849
\(176\) −3.11697 + 58.3062i −0.234951 + 4.39499i
\(177\) 0.00629823 0.000473404
\(178\) 13.8593 10.0694i 1.03880 0.754731i
\(179\) −4.22220 12.9946i −0.315582 0.971262i −0.975514 0.219937i \(-0.929415\pi\)
0.659932 0.751325i \(-0.270585\pi\)
\(180\) −4.96134 + 15.2694i −0.369796 + 1.13812i
\(181\) −5.39818 3.92201i −0.401244 0.291521i 0.368804 0.929507i \(-0.379767\pi\)
−0.770047 + 0.637987i \(0.779767\pi\)
\(182\) 9.23566 + 6.71010i 0.684593 + 0.497386i
\(183\) −3.04706 + 9.37790i −0.225245 + 0.693234i
\(184\) 22.7653 + 70.0643i 1.67828 + 5.16521i
\(185\) −0.724497 + 0.526378i −0.0532661 + 0.0387001i
\(186\) −2.23443 −0.163836
\(187\) 0.0952124 1.78105i 0.00696262 0.130243i
\(188\) −35.0043 −2.55295
\(189\) 3.31659 2.40964i 0.241246 0.175276i
\(190\) −1.13214 3.48438i −0.0821344 0.252784i
\(191\) 5.51100 16.9611i 0.398762 1.22726i −0.527231 0.849722i \(-0.676770\pi\)
0.925993 0.377540i \(-0.123230\pi\)
\(192\) −34.8524 25.3218i −2.51526 1.82744i
\(193\) −11.5104 8.36276i −0.828533 0.601965i 0.0906108 0.995886i \(-0.471118\pi\)
−0.919144 + 0.393922i \(0.871118\pi\)
\(194\) −3.11463 + 9.58584i −0.223617 + 0.688223i
\(195\) 0.862170 + 2.65349i 0.0617413 + 0.190020i
\(196\) −45.6522 + 33.1683i −3.26087 + 2.36916i
\(197\) 14.0364 1.00005 0.500025 0.866011i \(-0.333324\pi\)
0.500025 + 0.866011i \(0.333324\pi\)
\(198\) 8.92356 2.38104i 0.634170 0.169213i
\(199\) 4.48662 0.318048 0.159024 0.987275i \(-0.449165\pi\)
0.159024 + 0.987275i \(0.449165\pi\)
\(200\) 23.5507 17.1106i 1.66528 1.20990i
\(201\) −1.28094 3.94234i −0.0903509 0.278071i
\(202\) 11.2340 34.5747i 0.790422 2.43267i
\(203\) −8.97377 6.51983i −0.629835 0.457602i
\(204\) 2.50358 + 1.81896i 0.175286 + 0.127353i
\(205\) −2.85757 + 8.79471i −0.199582 + 0.614249i
\(206\) 2.38722 + 7.34711i 0.166326 + 0.511898i
\(207\) 5.70062 4.14175i 0.396221 0.287871i
\(208\) −17.6051 −1.22069
\(209\) −0.985513 + 1.21440i −0.0681694 + 0.0840020i
\(210\) −31.8508 −2.19792
\(211\) −6.81043 + 4.94807i −0.468850 + 0.340639i −0.796993 0.603989i \(-0.793577\pi\)
0.328143 + 0.944628i \(0.393577\pi\)
\(212\) −22.8072 70.1933i −1.56640 4.82089i
\(213\) −4.53959 + 13.9714i −0.311048 + 0.957306i
\(214\) −12.8348 9.32505i −0.877371 0.637447i
\(215\) 8.47512 + 6.15754i 0.577999 + 0.419941i
\(216\) −3.23079 + 9.94334i −0.219827 + 0.676559i
\(217\) −1.01650 3.12846i −0.0690044 0.212374i
\(218\) 0.638062 0.463579i 0.0432150 0.0313976i
\(219\) −14.1200 −0.954143
\(220\) −49.6924 19.1349i −3.35026 1.29007i
\(221\) 0.537773 0.0361745
\(222\) −0.723107 + 0.525368i −0.0485317 + 0.0352604i
\(223\) −4.78337 14.7217i −0.320318 0.985838i −0.973510 0.228646i \(-0.926570\pi\)
0.653191 0.757193i \(-0.273430\pi\)
\(224\) 35.6161 109.615i 2.37970 7.32397i
\(225\) −2.25257 1.63658i −0.150171 0.109106i
\(226\) 1.25365 + 0.910830i 0.0833916 + 0.0605875i
\(227\) 1.64702 5.06902i 0.109317 0.336443i −0.881402 0.472366i \(-0.843400\pi\)
0.990719 + 0.135923i \(0.0434001\pi\)
\(228\) −0.838535 2.58075i −0.0555333 0.170914i
\(229\) −15.0117 + 10.9066i −0.992002 + 0.720731i −0.960359 0.278768i \(-0.910074\pi\)
−0.0316432 + 0.999499i \(0.510074\pi\)
\(230\) −54.7459 −3.60984
\(231\) 7.39328 + 11.4108i 0.486442 + 0.750777i
\(232\) 28.2885 1.85723
\(233\) −10.6364 + 7.72780i −0.696814 + 0.506265i −0.878893 0.477019i \(-0.841717\pi\)
0.182079 + 0.983284i \(0.441717\pi\)
\(234\) 0.860515 + 2.64839i 0.0562537 + 0.173131i
\(235\) 5.24455 16.1411i 0.342117 1.05293i
\(236\) −0.0293212 0.0213031i −0.00190865 0.00138672i
\(237\) 0.867738 + 0.630449i 0.0563657 + 0.0409521i
\(238\) −1.89710 + 5.83869i −0.122971 + 0.378466i
\(239\) 7.08088 + 21.7927i 0.458024 + 1.40965i 0.867548 + 0.497353i \(0.165695\pi\)
−0.409524 + 0.912299i \(0.634305\pi\)
\(240\) 39.7380 28.8713i 2.56508 1.86364i
\(241\) 12.4123 0.799544 0.399772 0.916615i \(-0.369089\pi\)
0.399772 + 0.916615i \(0.369089\pi\)
\(242\) 6.30584 + 29.9755i 0.405355 + 1.92690i
\(243\) 1.00000 0.0641500
\(244\) 45.9053 33.3521i 2.93879 2.13515i
\(245\) −8.45456 26.0205i −0.540142 1.66239i
\(246\) −2.85209 + 8.77783i −0.181843 + 0.559654i
\(247\) −0.381496 0.277173i −0.0242740 0.0176361i
\(248\) 6.78694 + 4.93100i 0.430971 + 0.313119i
\(249\) 0.544497 1.67579i 0.0345061 0.106199i
\(250\) −5.31956 16.3719i −0.336438 1.03545i
\(251\) −4.67644 + 3.39763i −0.295174 + 0.214457i −0.725509 0.688213i \(-0.758396\pi\)
0.430335 + 0.902669i \(0.358396\pi\)
\(252\) −23.5907 −1.48607
\(253\) 12.7077 + 19.6132i 0.798928 + 1.23307i
\(254\) −59.8936 −3.75806
\(255\) −1.21385 + 0.881917i −0.0760145 + 0.0552278i
\(256\) 28.2202 + 86.8529i 1.76376 + 5.42830i
\(257\) −4.94015 + 15.2042i −0.308158 + 0.948412i 0.670322 + 0.742070i \(0.266156\pi\)
−0.978480 + 0.206342i \(0.933844\pi\)
\(258\) 8.45886 + 6.14572i 0.526626 + 0.382616i
\(259\) −1.06454 0.773430i −0.0661470 0.0480586i
\(260\) 4.96134 15.2694i 0.307689 0.946970i
\(261\) −0.836115 2.57330i −0.0517542 0.159283i
\(262\) 15.4984 11.2602i 0.957494 0.695660i
\(263\) −4.52538 −0.279047 −0.139524 0.990219i \(-0.544557\pi\)
−0.139524 + 0.990219i \(0.544557\pi\)
\(264\) −32.3593 12.4605i −1.99158 0.766890i
\(265\) 35.7844 2.19822
\(266\) 4.35513 3.16418i 0.267030 0.194009i
\(267\) 1.90103 + 5.85078i 0.116341 + 0.358062i
\(268\) −7.37117 + 22.6861i −0.450266 + 1.38578i
\(269\) −4.73572 3.44070i −0.288742 0.209783i 0.433979 0.900923i \(-0.357109\pi\)
−0.722721 + 0.691139i \(0.757109\pi\)
\(270\) −6.28557 4.56673i −0.382527 0.277922i
\(271\) −4.33812 + 13.3514i −0.263522 + 0.811037i 0.728508 + 0.685037i \(0.240214\pi\)
−0.992030 + 0.126000i \(0.959786\pi\)
\(272\) −2.92563 9.00415i −0.177392 0.545957i
\(273\) −3.31659 + 2.40964i −0.200729 + 0.145838i
\(274\) −34.5005 −2.08425
\(275\) 5.81901 7.17051i 0.350900 0.432398i
\(276\) −40.5481 −2.44071
\(277\) −4.57455 + 3.32361i −0.274858 + 0.199696i −0.716672 0.697411i \(-0.754335\pi\)
0.441813 + 0.897107i \(0.354335\pi\)
\(278\) 15.0588 + 46.3464i 0.903169 + 2.77967i
\(279\) 0.247955 0.763127i 0.0148447 0.0456872i
\(280\) 96.7449 + 70.2893i 5.78161 + 4.20059i
\(281\) 16.8975 + 12.2767i 1.00802 + 0.732369i 0.963793 0.266652i \(-0.0859174\pi\)
0.0442272 + 0.999021i \(0.485917\pi\)
\(282\) 5.23448 16.1101i 0.311709 0.959342i
\(283\) 6.13883 + 18.8934i 0.364916 + 1.12309i 0.950034 + 0.312147i \(0.101048\pi\)
−0.585118 + 0.810948i \(0.698952\pi\)
\(284\) 68.3909 49.6889i 4.05825 2.94849i
\(285\) 1.31566 0.0779329
\(286\) −8.92356 + 2.38104i −0.527661 + 0.140794i
\(287\) −13.5875 −0.802043
\(288\) 22.7451 16.5253i 1.34027 0.973762i
\(289\) −5.16392 15.8929i −0.303760 0.934877i
\(290\) −6.49610 + 19.9929i −0.381464 + 1.17403i
\(291\) −2.92823 2.12748i −0.171656 0.124715i
\(292\) 65.7354 + 47.7596i 3.84687 + 2.79492i
\(293\) 9.18143 28.2575i 0.536385 1.65082i −0.204253 0.978918i \(-0.565477\pi\)
0.740638 0.671904i \(-0.234523\pi\)
\(294\) −8.43833 25.9705i −0.492134 1.51463i
\(295\) 0.0142163 0.0103288i 0.000827706 0.000601363i
\(296\) 3.35579 0.195051
\(297\) −0.177050 + 3.31190i −0.0102735 + 0.192176i
\(298\) 23.8177 1.37972
\(299\) −5.70062 + 4.14175i −0.329676 + 0.239523i
\(300\) 4.95117 + 15.2381i 0.285856 + 0.879775i
\(301\) −4.75657 + 14.6392i −0.274164 + 0.843791i
\(302\) 26.5314 + 19.2762i 1.52671 + 1.10922i
\(303\) 10.5617 + 7.67352i 0.606754 + 0.440832i
\(304\) −2.56539 + 7.89545i −0.147135 + 0.452835i
\(305\) 8.50143 + 26.1647i 0.486790 + 1.49819i
\(306\) −1.21153 + 0.880225i −0.0692583 + 0.0503191i
\(307\) −9.70302 −0.553781 −0.276890 0.960902i \(-0.589304\pi\)
−0.276890 + 0.960902i \(0.589304\pi\)
\(308\) 4.17672 78.1298i 0.237990 4.45186i
\(309\) −2.77418 −0.157817
\(310\) −5.04353 + 3.66434i −0.286453 + 0.208121i
\(311\) 0.774571 + 2.38389i 0.0439219 + 0.135178i 0.970613 0.240647i \(-0.0773595\pi\)
−0.926691 + 0.375825i \(0.877360\pi\)
\(312\) 3.23079 9.94334i 0.182907 0.562931i
\(313\) −24.9880 18.1548i −1.41240 1.02617i −0.992968 0.118386i \(-0.962228\pi\)
−0.419436 0.907785i \(-0.637772\pi\)
\(314\) −20.9324 15.2083i −1.18128 0.858253i
\(315\) 3.53449 10.8780i 0.199146 0.612908i
\(316\) −1.90730 5.87007i −0.107294 0.330217i
\(317\) −2.33944 + 1.69970i −0.131396 + 0.0954648i −0.651542 0.758613i \(-0.725878\pi\)
0.520146 + 0.854077i \(0.325878\pi\)
\(318\) 35.7157 2.00284
\(319\) 8.67052 2.31352i 0.485456 0.129532i
\(320\) −120.195 −6.71909
\(321\) 4.60908 3.34869i 0.257254 0.186906i
\(322\) −24.8575 76.5035i −1.38525 4.26337i
\(323\) 0.0783635 0.241178i 0.00436026 0.0134195i
\(324\) −4.65547 3.38240i −0.258637 0.187911i
\(325\) 2.25257 + 1.63658i 0.124950 + 0.0907814i
\(326\) 19.5893 60.2896i 1.08495 3.33913i
\(327\) 0.0875209 + 0.269361i 0.00483991 + 0.0148957i
\(328\) 28.0342 20.3680i 1.54793 1.12464i
\(329\) 24.9373 1.37484
\(330\) 16.2374 20.0086i 0.893839 1.10144i
\(331\) −13.4774 −0.740785 −0.370392 0.928875i \(-0.620777\pi\)
−0.370392 + 0.928875i \(0.620777\pi\)
\(332\) −8.20308 + 5.95989i −0.450203 + 0.327091i
\(333\) −0.0991861 0.305263i −0.00543536 0.0167283i
\(334\) −6.07451 + 18.6954i −0.332382 + 1.02297i
\(335\) −9.35656 6.79794i −0.511203 0.371411i
\(336\) 58.3888 + 42.4219i 3.18537 + 2.31431i
\(337\) −6.66618 + 20.5164i −0.363130 + 1.11760i 0.588014 + 0.808851i \(0.299910\pi\)
−0.951144 + 0.308749i \(0.900090\pi\)
\(338\) −0.860515 2.64839i −0.0468059 0.144054i
\(339\) −0.450194 + 0.327085i −0.0244512 + 0.0177648i
\(340\) 8.63406 0.468248
\(341\) 2.48350 + 0.956312i 0.134489 + 0.0517872i
\(342\) 1.31313 0.0710062
\(343\) 9.30681 6.76179i 0.502520 0.365102i
\(344\) −12.1307 37.3345i −0.654044 2.01294i
\(345\) 6.07516 18.6974i 0.327075 1.00663i
\(346\) −17.9554 13.0453i −0.965286 0.701322i
\(347\) −22.4397 16.3034i −1.20463 0.875214i −0.209896 0.977724i \(-0.567313\pi\)
−0.994732 + 0.102510i \(0.967313\pi\)
\(348\) −4.81140 + 14.8080i −0.257918 + 0.793791i
\(349\) 3.59928 + 11.0774i 0.192665 + 0.592961i 0.999996 + 0.00286254i \(0.000911177\pi\)
−0.807331 + 0.590099i \(0.799089\pi\)
\(350\) −25.7151 + 18.6831i −1.37453 + 0.998653i
\(351\) −1.00000 −0.0533761
\(352\) 50.7030 + 78.2553i 2.70248 + 4.17102i
\(353\) 23.2708 1.23858 0.619291 0.785161i \(-0.287420\pi\)
0.619291 + 0.785161i \(0.287420\pi\)
\(354\) 0.0141890 0.0103089i 0.000754138 0.000547914i
\(355\) 12.6656 + 38.9808i 0.672223 + 2.06889i
\(356\) 10.9395 33.6682i 0.579790 1.78441i
\(357\) −1.78357 1.29584i −0.0943966 0.0685831i
\(358\) −30.7816 22.3641i −1.62686 1.18198i
\(359\) −9.21852 + 28.3717i −0.486535 + 1.49740i 0.343211 + 0.939258i \(0.388485\pi\)
−0.829746 + 0.558142i \(0.811515\pi\)
\(360\) 9.01403 + 27.7423i 0.475081 + 1.46215i
\(361\) 15.1914 11.0372i 0.799549 0.580906i
\(362\) −18.5809 −0.976589
\(363\) −10.9373 1.17274i −0.574060 0.0615529i
\(364\) 23.5907 1.23649
\(365\) −31.8716 + 23.1561i −1.66824 + 1.21204i
\(366\) 8.48512 + 26.1145i 0.443524 + 1.36503i
\(367\) −2.85508 + 8.78702i −0.149034 + 0.458679i −0.997508 0.0705585i \(-0.977522\pi\)
0.848474 + 0.529237i \(0.177522\pi\)
\(368\) 100.360 + 72.9157i 5.23162 + 3.80099i
\(369\) −2.68140 1.94815i −0.139588 0.101417i
\(370\) −0.770615 + 2.37171i −0.0400624 + 0.123299i
\(371\) 16.2480 + 50.0061i 0.843553 + 2.59619i
\(372\) −3.73555 + 2.71403i −0.193679 + 0.140716i
\(373\) 9.45574 0.489600 0.244800 0.969574i \(-0.421278\pi\)
0.244800 + 0.969574i \(0.421278\pi\)
\(374\) −2.70071 4.16829i −0.139651 0.215537i
\(375\) 6.18182 0.319228
\(376\) −51.4516 + 37.3818i −2.65341 + 1.92782i
\(377\) 0.836115 + 2.57330i 0.0430621 + 0.132532i
\(378\) 3.52771 10.8572i 0.181446 0.558433i
\(379\) −9.22696 6.70378i −0.473957 0.344350i 0.325024 0.945706i \(-0.394627\pi\)
−0.798981 + 0.601356i \(0.794627\pi\)
\(380\) −6.12501 4.45008i −0.314207 0.228284i
\(381\) 6.64640 20.4555i 0.340505 1.04797i
\(382\) −15.3464 47.2313i −0.785190 2.41657i
\(383\) 28.9202 21.0117i 1.47775 1.07365i 0.499480 0.866325i \(-0.333524\pi\)
0.978272 0.207325i \(-0.0664756\pi\)
\(384\) −63.7352 −3.25247
\(385\) 35.4012 + 13.6318i 1.80421 + 0.694742i
\(386\) −39.6193 −2.01657
\(387\) −3.03763 + 2.20697i −0.154412 + 0.112187i
\(388\) 6.43630 + 19.8089i 0.326753 + 1.00564i
\(389\) −3.39313 + 10.4430i −0.172038 + 0.529480i −0.999486 0.0320634i \(-0.989792\pi\)
0.827447 + 0.561543i \(0.189792\pi\)
\(390\) 6.28557 + 4.56673i 0.318282 + 0.231245i
\(391\) −3.06564 2.22732i −0.155036 0.112640i
\(392\) −31.6815 + 97.5058i −1.60016 + 4.92479i
\(393\) 2.12586 + 6.54273i 0.107236 + 0.330037i
\(394\) 31.6220 22.9747i 1.59309 1.15745i
\(395\) 2.99255 0.150572
\(396\) 12.0264 14.8196i 0.604349 0.744712i
\(397\) −8.71624 −0.437456 −0.218728 0.975786i \(-0.570191\pi\)
−0.218728 + 0.975786i \(0.570191\pi\)
\(398\) 10.1077 7.34369i 0.506655 0.368106i
\(399\) 0.597378 + 1.83854i 0.0299063 + 0.0920421i
\(400\) 15.1475 46.6191i 0.757373 2.33096i
\(401\) −26.9918 19.6107i −1.34791 0.979311i −0.999113 0.0421114i \(-0.986592\pi\)
−0.348793 0.937200i \(-0.613408\pi\)
\(402\) −9.33861 6.78489i −0.465767 0.338400i
\(403\) −0.247955 + 0.763127i −0.0123515 + 0.0380141i
\(404\) −23.2148 71.4477i −1.15498 3.55466i
\(405\) 2.25719 1.63994i 0.112161 0.0814895i
\(406\) −30.8883 −1.53296
\(407\) 1.02856 0.274447i 0.0509839 0.0136038i
\(408\) 5.62244 0.278352
\(409\) 27.1252 19.7076i 1.34126 0.974480i 0.341860 0.939751i \(-0.388943\pi\)
0.999397 0.0347288i \(-0.0110568\pi\)
\(410\) 7.95744 + 24.4905i 0.392990 + 1.20950i
\(411\) 3.82853 11.7830i 0.188847 0.581212i
\(412\) 12.9151 + 9.38337i 0.636281 + 0.462285i
\(413\) 0.0208887 + 0.0151765i 0.00102786 + 0.000746786i
\(414\) 6.06350 18.6615i 0.298005 0.917164i
\(415\) −1.51917 4.67552i −0.0745731 0.229512i
\(416\) −22.7451 + 16.5253i −1.11517 + 0.810219i
\(417\) −17.4998 −0.856969
\(418\) −0.232490 + 4.34896i −0.0113715 + 0.212715i
\(419\) 8.26093 0.403573 0.201786 0.979430i \(-0.435325\pi\)
0.201786 + 0.979430i \(0.435325\pi\)
\(420\) −53.2486 + 38.6874i −2.59827 + 1.88775i
\(421\) −2.20317 6.78065i −0.107376 0.330469i 0.882905 0.469552i \(-0.155585\pi\)
−0.990281 + 0.139083i \(0.955585\pi\)
\(422\) −7.24396 + 22.2946i −0.352630 + 1.08528i
\(423\) 4.92122 + 3.57548i 0.239278 + 0.173846i
\(424\) −108.484 78.8184i −5.26846 3.82776i
\(425\) −0.462701 + 1.42405i −0.0224443 + 0.0690765i
\(426\) 12.6413 + 38.9060i 0.612475 + 1.88500i
\(427\) −32.7032 + 23.7603i −1.58262 + 1.14984i
\(428\) −32.7840 −1.58468
\(429\) 0.177050 3.31190i 0.00854804 0.159900i
\(430\) 29.1719 1.40679
\(431\) 20.2346 14.7013i 0.974666 0.708136i 0.0181557 0.999835i \(-0.494221\pi\)
0.956510 + 0.291699i \(0.0942205\pi\)
\(432\) 5.44027 + 16.7434i 0.261745 + 0.805568i
\(433\) −4.05466 + 12.4790i −0.194855 + 0.599701i 0.805124 + 0.593107i \(0.202099\pi\)
−0.999978 + 0.00659404i \(0.997901\pi\)
\(434\) −7.41069 5.38418i −0.355724 0.258449i
\(435\) −6.10733 4.43724i −0.292824 0.212749i
\(436\) 0.503637 1.55004i 0.0241198 0.0742332i
\(437\) 1.02679 + 3.16012i 0.0491178 + 0.151169i
\(438\) −31.8104 + 23.1116i −1.51996 + 1.10432i
\(439\) −23.2672 −1.11048 −0.555242 0.831689i \(-0.687374\pi\)
−0.555242 + 0.831689i \(0.687374\pi\)
\(440\) −93.4756 + 24.9417i −4.45627 + 1.18905i
\(441\) 9.80614 0.466959
\(442\) 1.21153 0.880225i 0.0576264 0.0418680i
\(443\) 10.1396 + 31.2065i 0.481748 + 1.48267i 0.836637 + 0.547758i \(0.184519\pi\)
−0.354889 + 0.934908i \(0.615481\pi\)
\(444\) −0.570764 + 1.75663i −0.0270873 + 0.0833661i
\(445\) 13.8859 + 10.0887i 0.658257 + 0.478252i
\(446\) −34.8727 25.3365i −1.65127 1.19972i
\(447\) −2.64305 + 8.13447i −0.125012 + 0.384747i
\(448\) −54.5747 167.964i −2.57841 7.93554i
\(449\) −14.4756 + 10.5172i −0.683148 + 0.496336i −0.874401 0.485205i \(-0.838745\pi\)
0.191253 + 0.981541i \(0.438745\pi\)
\(450\) −7.75347 −0.365502
\(451\) 6.92682 8.53561i 0.326171 0.401926i
\(452\) 3.20220 0.150619
\(453\) −9.52761 + 6.92221i −0.447646 + 0.325234i
\(454\) −4.58645 14.1156i −0.215253 0.662480i
\(455\) −3.53449 + 10.8780i −0.165699 + 0.509971i
\(456\) −3.98856 2.89786i −0.186782 0.135705i
\(457\) 17.6397 + 12.8160i 0.825152 + 0.599508i 0.918184 0.396155i \(-0.129656\pi\)
−0.0930317 + 0.995663i \(0.529656\pi\)
\(458\) −15.9673 + 49.1423i −0.746102 + 2.29627i
\(459\) −0.166181 0.511452i −0.00775666 0.0238725i
\(460\) −91.5248 + 66.4967i −4.26737 + 3.10042i
\(461\) 15.4094 0.717688 0.358844 0.933398i \(-0.383171\pi\)
0.358844 + 0.933398i \(0.383171\pi\)
\(462\) 35.3332 + 13.6057i 1.64385 + 0.632993i
\(463\) 31.2592 1.45274 0.726369 0.687305i \(-0.241206\pi\)
0.726369 + 0.687305i \(0.241206\pi\)
\(464\) 38.5371 27.9988i 1.78904 1.29981i
\(465\) −0.691804 2.12916i −0.0320817 0.0987372i
\(466\) −11.3135 + 34.8193i −0.524087 + 1.61297i
\(467\) 10.6569 + 7.74267i 0.493141 + 0.358288i 0.806391 0.591383i \(-0.201418\pi\)
−0.313250 + 0.949671i \(0.601418\pi\)
\(468\) 4.65547 + 3.38240i 0.215199 + 0.156351i
\(469\) 5.25127 16.1618i 0.242481 0.746280i
\(470\) −14.6044 44.9478i −0.673652 2.07329i
\(471\) 7.51697 5.46140i 0.346364 0.251648i
\(472\) −0.0658483 −0.00303092
\(473\) −6.77145 10.4511i −0.311351 0.480541i
\(474\) 2.98681 0.137189
\(475\) 1.06221 0.771741i 0.0487375 0.0354099i
\(476\) 3.92032 + 12.0655i 0.179687 + 0.553021i
\(477\) −3.96338 + 12.1980i −0.181471 + 0.558509i
\(478\) 51.6224 + 37.5059i 2.36116 + 1.71548i
\(479\) −10.1560 7.37876i −0.464039 0.337144i 0.331075 0.943605i \(-0.392589\pi\)
−0.795114 + 0.606461i \(0.792589\pi\)
\(480\) 24.2395 74.6015i 1.10638 3.40508i
\(481\) 0.0991861 + 0.305263i 0.00452250 + 0.0139188i
\(482\) 27.9631 20.3164i 1.27368 0.925385i
\(483\) 28.8868 1.31439
\(484\) 46.9516 + 42.4540i 2.13417 + 1.92973i
\(485\) −10.0985 −0.458551
\(486\) 2.25286 1.63680i 0.102192 0.0742467i
\(487\) 2.44119 + 7.51320i 0.110621 + 0.340455i 0.991008 0.133799i \(-0.0427177\pi\)
−0.880388 + 0.474254i \(0.842718\pi\)
\(488\) 31.8572 98.0463i 1.44211 4.43835i
\(489\) 18.4169 + 13.3807i 0.832843 + 0.605096i
\(490\) −61.6371 44.7820i −2.78448 2.02304i
\(491\) −0.633004 + 1.94818i −0.0285671 + 0.0879203i −0.964324 0.264727i \(-0.914718\pi\)
0.935756 + 0.352647i \(0.114718\pi\)
\(492\) 5.89377 + 18.1391i 0.265711 + 0.817776i
\(493\) −1.17717 + 0.855265i −0.0530171 + 0.0385192i
\(494\) −1.31313 −0.0590807
\(495\) 5.03169 + 7.76593i 0.226158 + 0.349053i
\(496\) 14.1263 0.634289
\(497\) −48.7221 + 35.3987i −2.18549 + 1.58785i
\(498\) −1.51625 4.66655i −0.0679450 0.209113i
\(499\) −7.95426 + 24.4807i −0.356082 + 1.09591i 0.599298 + 0.800526i \(0.295447\pi\)
−0.955380 + 0.295381i \(0.904553\pi\)
\(500\) −28.7793 20.9094i −1.28705 0.935096i
\(501\) −5.71097 4.14926i −0.255147 0.185375i
\(502\) −4.97412 + 15.3088i −0.222006 + 0.683264i
\(503\) −6.59639 20.3016i −0.294119 0.905204i −0.983516 0.180821i \(-0.942125\pi\)
0.689398 0.724383i \(-0.257875\pi\)
\(504\) −34.6751 + 25.1929i −1.54455 + 1.12218i
\(505\) 36.4239 1.62084
\(506\) 60.7315 + 23.3857i 2.69985 + 1.03962i
\(507\) 1.00000 0.0444116
\(508\) −100.131 + 72.7493i −4.44259 + 3.22773i
\(509\) 5.20633 + 16.0234i 0.230766 + 0.710226i 0.997655 + 0.0684456i \(0.0218040\pi\)
−0.766888 + 0.641780i \(0.778196\pi\)
\(510\) −1.29112 + 3.97367i −0.0571719 + 0.175957i
\(511\) −46.8303 34.0242i −2.07165 1.50514i
\(512\) 102.611 + 74.5513i 4.53481 + 3.29473i
\(513\) −0.145719 + 0.448476i −0.00643364 + 0.0198007i
\(514\) 13.7568 + 42.3389i 0.606785 + 1.86749i
\(515\) −6.26184 + 4.54949i −0.275930 + 0.200475i
\(516\) 21.6065 0.951172
\(517\) −12.7129 + 15.6655i −0.559113 + 0.688969i
\(518\) −3.66420 −0.160996
\(519\) 6.44790 4.68467i 0.283031 0.205634i
\(520\) −9.01403 27.7423i −0.395291 1.21658i
\(521\) −0.429309 + 1.32128i −0.0188084 + 0.0578863i −0.960020 0.279931i \(-0.909688\pi\)
0.941212 + 0.337817i \(0.109688\pi\)
\(522\) −6.09561 4.42872i −0.266798 0.193840i
\(523\) 0.718852 + 0.522276i 0.0314332 + 0.0228376i 0.603391 0.797446i \(-0.293816\pi\)
−0.571958 + 0.820283i \(0.693816\pi\)
\(524\) 12.2332 37.6500i 0.534411 1.64475i
\(525\) −3.52725 10.8558i −0.153942 0.473784i
\(526\) −10.1950 + 7.40713i −0.444525 + 0.322966i
\(527\) −0.431508 −0.0187968
\(528\) −56.4157 + 15.0532i −2.45518 + 0.655106i
\(529\) 26.6512 1.15875
\(530\) 80.6172 58.5718i 3.50179 2.54420i
\(531\) 0.00194626 + 0.00598998i 8.44605e−5 + 0.000259943i
\(532\) 3.43760 10.5798i 0.149039 0.458694i
\(533\) 2.68140 + 1.94815i 0.116144 + 0.0843839i
\(534\) 13.8593 + 10.0694i 0.599750 + 0.435744i
\(535\) 4.91190 15.1173i 0.212360 0.653576i
\(536\) 13.3923 + 41.2174i 0.578461 + 1.78032i
\(537\) 11.0539 8.03110i 0.477010 0.346568i
\(538\) −16.3006 −0.702771
\(539\) −1.73617 + 32.4769i −0.0747823 + 1.39888i
\(540\) −16.0552 −0.690907
\(541\) 11.3076 8.21548i 0.486154 0.353211i −0.317550 0.948242i \(-0.602860\pi\)
0.803703 + 0.595030i \(0.202860\pi\)
\(542\) 12.0803 + 37.1793i 0.518893 + 1.59699i
\(543\) 2.06192 6.34594i 0.0884855 0.272330i
\(544\) −12.2317 8.88685i −0.524430 0.381021i
\(545\) 0.639289 + 0.464471i 0.0273841 + 0.0198957i
\(546\) −3.52771 + 10.8572i −0.150972 + 0.464644i
\(547\) 0.0977966 + 0.300987i 0.00418148 + 0.0128693i 0.953125 0.302575i \(-0.0978464\pi\)
−0.948944 + 0.315445i \(0.897846\pi\)
\(548\) −57.6784 + 41.9058i −2.46390 + 1.79013i
\(549\) −9.86050 −0.420836
\(550\) 1.37275 25.6787i 0.0585342 1.09494i
\(551\) 1.27590 0.0543551
\(552\) −59.6003 + 43.3021i −2.53676 + 1.84306i
\(553\) 1.35877 + 4.18188i 0.0577810 + 0.177832i
\(554\) −4.86575 + 14.9752i −0.206726 + 0.636236i
\(555\) −0.724497 0.526378i −0.0307532 0.0223435i
\(556\) 81.4698 + 59.1913i 3.45509 + 2.51027i
\(557\) 11.0442 33.9904i 0.467956 1.44022i −0.387270 0.921966i \(-0.626582\pi\)
0.855226 0.518255i \(-0.173418\pi\)
\(558\) −0.690477 2.12507i −0.0292302 0.0899614i
\(559\) 3.03763 2.20697i 0.128478 0.0933449i
\(560\) 201.364 8.50919
\(561\) 1.72330 0.459821i 0.0727577 0.0194137i
\(562\) 58.1622 2.45343
\(563\) −30.1356 + 21.8948i −1.27006 + 0.922755i −0.999205 0.0398643i \(-0.987307\pi\)
−0.270858 + 0.962619i \(0.587307\pi\)
\(564\) −10.8169 33.2911i −0.455474 1.40181i
\(565\) −0.479772 + 1.47659i −0.0201842 + 0.0621205i
\(566\) 44.7546 + 32.5161i 1.88117 + 1.36675i
\(567\) 3.31659 + 2.40964i 0.139284 + 0.101195i
\(568\) 47.4616 146.072i 1.99145 6.12904i
\(569\) −2.44848 7.53565i −0.102646 0.315911i 0.886525 0.462681i \(-0.153112\pi\)
−0.989171 + 0.146770i \(0.953112\pi\)
\(570\) 2.96399 2.15347i 0.124148 0.0901988i
\(571\) 4.43525 0.185609 0.0928047 0.995684i \(-0.470417\pi\)
0.0928047 + 0.995684i \(0.470417\pi\)
\(572\) −12.0264 + 14.8196i −0.502849 + 0.619638i
\(573\) 17.8340 0.745024
\(574\) −30.6106 + 22.2399i −1.27766 + 0.928277i
\(575\) −6.06271 18.6591i −0.252833 0.778139i
\(576\) 13.3124 40.9715i 0.554685 1.70714i
\(577\) 8.96744 + 6.51522i 0.373319 + 0.271232i 0.758586 0.651573i \(-0.225891\pi\)
−0.385267 + 0.922805i \(0.625891\pi\)
\(578\) −37.6471 27.3522i −1.56591 1.13770i
\(579\) 4.39656 13.5312i 0.182715 0.562339i
\(580\) 13.4240 + 41.3149i 0.557402 + 1.71551i
\(581\) 5.84393 4.24586i 0.242447 0.176148i
\(582\) −10.0792 −0.417794
\(583\) −39.6969 15.2859i −1.64408 0.633079i
\(584\) 147.626 6.10879
\(585\) −2.25719 + 1.63994i −0.0933233 + 0.0678034i
\(586\) −25.5674 78.6884i −1.05618 3.25059i
\(587\) −6.14070 + 18.8991i −0.253454 + 0.780051i 0.740676 + 0.671862i \(0.234505\pi\)
−0.994130 + 0.108189i \(0.965495\pi\)
\(588\) −45.6522 33.1683i −1.88266 1.36784i
\(589\) 0.306112 + 0.222404i 0.0126131 + 0.00916399i
\(590\) 0.0151213 0.0465384i 0.000622532 0.00191596i
\(591\) 4.33748 + 13.3494i 0.178420 + 0.549120i
\(592\) 4.57155 3.32143i 0.187890 0.136510i
\(593\) 23.1858 0.952127 0.476064 0.879411i \(-0.342063\pi\)
0.476064 + 0.879411i \(0.342063\pi\)
\(594\) 5.02204 + 7.75103i 0.206057 + 0.318029i
\(595\) −6.15096 −0.252165
\(596\) 39.8187 28.9300i 1.63104 1.18502i
\(597\) 1.38644 + 4.26703i 0.0567433 + 0.174638i
\(598\) −6.06350 + 18.6615i −0.247955 + 0.763127i
\(599\) −16.4590 11.9582i −0.672498 0.488598i 0.198362 0.980129i \(-0.436438\pi\)
−0.870860 + 0.491530i \(0.836438\pi\)
\(600\) 23.5507 + 17.1106i 0.961453 + 0.698536i
\(601\) 7.28686 22.4267i 0.297237 0.914802i −0.685224 0.728333i \(-0.740295\pi\)
0.982461 0.186469i \(-0.0597045\pi\)
\(602\) 13.2456 + 40.7657i 0.539849 + 1.66148i
\(603\) 3.35356 2.43650i 0.136567 0.0992220i
\(604\) 67.7692 2.75749
\(605\) −26.6108 + 15.2895i −1.08188 + 0.621606i
\(606\) 36.3540 1.47678
\(607\) −3.36147 + 2.44225i −0.136438 + 0.0991278i −0.653911 0.756572i \(-0.726873\pi\)
0.517473 + 0.855700i \(0.326873\pi\)
\(608\) 4.09681 + 12.6087i 0.166148 + 0.511350i
\(609\) 3.42768 10.5493i 0.138896 0.427479i
\(610\) 61.9788 + 45.0303i 2.50945 + 1.82322i
\(611\) −4.92122 3.57548i −0.199091 0.144648i
\(612\) −0.956284 + 2.94314i −0.0386555 + 0.118969i
\(613\) 3.02768 + 9.31824i 0.122287 + 0.376360i 0.993397 0.114728i \(-0.0365995\pi\)
−0.871110 + 0.491088i \(0.836599\pi\)
\(614\) −21.8595 + 15.8819i −0.882179 + 0.640941i
\(615\) −9.24730 −0.372887
\(616\) −77.2971 119.301i −3.11439 4.80676i
\(617\) −11.1642 −0.449454 −0.224727 0.974422i \(-0.572149\pi\)
−0.224727 + 0.974422i \(0.572149\pi\)
\(618\) −6.24983 + 4.54076i −0.251405 + 0.182656i
\(619\) 11.0089 + 33.8820i 0.442486 + 1.36183i 0.885217 + 0.465178i \(0.154010\pi\)
−0.442731 + 0.896655i \(0.645990\pi\)
\(620\) −3.98097 + 12.2522i −0.159880 + 0.492059i
\(621\) 5.70062 + 4.14175i 0.228758 + 0.166203i
\(622\) 5.64694 + 4.10274i 0.226422 + 0.164505i
\(623\) −7.79334 + 23.9854i −0.312234 + 0.960956i
\(624\) −5.44027 16.7434i −0.217785 0.670273i
\(625\) 25.2164 18.3208i 1.00866 0.732831i
\(626\) −86.0101 −3.43766
\(627\) −1.45951 0.562008i −0.0582871 0.0224444i
\(628\) −53.4677 −2.13359
\(629\) −0.139645 + 0.101458i −0.00556800 + 0.00404539i
\(630\) −9.84245 30.2919i −0.392133 1.20686i
\(631\) −1.66580 + 5.12680i −0.0663144 + 0.204095i −0.978723 0.205186i \(-0.934220\pi\)
0.912409 + 0.409280i \(0.134220\pi\)
\(632\) −9.07225 6.59137i −0.360875 0.262191i
\(633\) −6.81043 4.94807i −0.270690 0.196668i
\(634\) −2.48836 + 7.65838i −0.0988253 + 0.304153i
\(635\) −18.5437 57.0717i −0.735885 2.26482i
\(636\) 59.7100 43.3818i 2.36765 1.72020i
\(637\) −9.80614 −0.388533
\(638\) 15.7467 19.4039i 0.623418 0.768209i
\(639\) −14.6904 −0.581144
\(640\) −143.862 + 104.522i −5.68666 + 4.13160i
\(641\) 10.0690 + 30.9891i 0.397700 + 1.22399i 0.926839 + 0.375459i \(0.122515\pi\)
−0.529139 + 0.848535i \(0.677485\pi\)
\(642\) 4.90247 15.0883i 0.193485 0.595486i
\(643\) −4.88539 3.54945i −0.192661 0.139976i 0.487273 0.873250i \(-0.337992\pi\)
−0.679934 + 0.733273i \(0.737992\pi\)
\(644\) −134.481 97.7065i −5.29931 3.85017i
\(645\) −3.23721 + 9.96310i −0.127465 + 0.392297i
\(646\) −0.218218 0.671605i −0.00858566 0.0264240i
\(647\) 28.8413 20.9544i 1.13387 0.823804i 0.147615 0.989045i \(-0.452840\pi\)
0.986253 + 0.165241i \(0.0528403\pi\)
\(648\) −10.4550 −0.410713
\(649\) −0.0201828 + 0.00538529i −0.000792243 + 0.000211391i
\(650\) 7.75347 0.304116
\(651\) 2.66123 1.93350i 0.104302 0.0757797i
\(652\) −40.4807 124.587i −1.58535 4.87920i
\(653\) −3.11773 + 9.59539i −0.122006 + 0.375497i −0.993344 0.115187i \(-0.963253\pi\)
0.871337 + 0.490684i \(0.163253\pi\)
\(654\) 0.638062 + 0.463579i 0.0249502 + 0.0181274i
\(655\) 15.5282 + 11.2819i 0.606737 + 0.440820i
\(656\) 18.0312 55.4943i 0.704000 2.16669i
\(657\) −4.36333 13.4289i −0.170230 0.523913i
\(658\) 56.1802 40.8173i 2.19013 1.59122i
\(659\) −23.8252 −0.928096 −0.464048 0.885810i \(-0.653604\pi\)
−0.464048 + 0.885810i \(0.653604\pi\)
\(660\) 2.84257 53.1732i 0.110647 2.06977i
\(661\) 5.03023 0.195653 0.0978266 0.995203i \(-0.468811\pi\)
0.0978266 + 0.995203i \(0.468811\pi\)
\(662\) −30.3627 + 22.0598i −1.18008 + 0.857377i
\(663\) 0.166181 + 0.511452i 0.00645393 + 0.0198632i
\(664\) −5.69274 + 17.5205i −0.220921 + 0.679926i
\(665\) 4.36350 + 3.17027i 0.169209 + 0.122938i
\(666\) −0.723107 0.525368i −0.0280198 0.0203576i
\(667\) 5.89156 18.1324i 0.228122 0.702088i
\(668\) 12.5528 + 38.6336i 0.485683 + 1.49478i
\(669\) 12.5230 9.09851i 0.484168 0.351769i
\(670\) −32.2059 −1.24422
\(671\) 1.74580 32.6570i 0.0673958 1.26071i
\(672\) 115.256 4.44611
\(673\) −6.61951 + 4.80935i −0.255163 + 0.185387i −0.708012 0.706200i \(-0.750408\pi\)
0.452849 + 0.891587i \(0.350408\pi\)
\(674\) 18.5632 + 57.1317i 0.715029 + 2.20063i
\(675\) 0.860404 2.64805i 0.0331169 0.101923i
\(676\) −4.65547 3.38240i −0.179057 0.130092i
\(677\) −35.8450 26.0429i −1.37763 1.00091i −0.997097 0.0761442i \(-0.975739\pi\)
−0.380537 0.924766i \(-0.624261\pi\)
\(678\) −0.478852 + 1.47375i −0.0183902 + 0.0565992i
\(679\) −4.58526 14.1120i −0.175966 0.541568i
\(680\) 12.6909 9.22049i 0.486674 0.353589i
\(681\) 5.32988 0.204242
\(682\) 7.16026 1.91055i 0.274180 0.0731586i
\(683\) 4.88202 0.186805 0.0934026 0.995628i \(-0.470226\pi\)
0.0934026 + 0.995628i \(0.470226\pi\)
\(684\) 2.19531 1.59499i 0.0839399 0.0609859i
\(685\) −10.6817 32.8750i −0.408128 1.25609i
\(686\) 9.89924 30.4667i 0.377955 1.16323i
\(687\) −15.0117 10.9066i −0.572732 0.416114i
\(688\) −53.4778 38.8539i −2.03882 1.48129i
\(689\) 3.96338 12.1980i 0.150993 0.464708i
\(690\) −16.9174 52.0664i −0.644035 1.98214i
\(691\) 11.4661 8.33063i 0.436192 0.316912i −0.347928 0.937521i \(-0.613115\pi\)
0.784120 + 0.620609i \(0.213115\pi\)
\(692\) −45.8634 −1.74347
\(693\) −8.56769 + 10.5576i −0.325459 + 0.401049i
\(694\) −77.2390 −2.93195
\(695\) −39.5004 + 28.6987i −1.49833 + 1.08860i
\(696\) 8.74162 + 26.9039i 0.331350 + 1.01979i
\(697\) −0.550789 + 1.69516i −0.0208626 + 0.0642086i
\(698\) 26.2402 + 19.0646i 0.993205 + 0.721606i
\(699\) −10.6364 7.72780i −0.402306 0.292292i
\(700\) −20.2975 + 62.4692i −0.767173 + 2.36111i
\(701\) −8.79806 27.0777i −0.332298 1.02271i −0.968038 0.250805i \(-0.919305\pi\)
0.635739 0.771904i \(-0.280695\pi\)
\(702\) −2.25286 + 1.63680i −0.0850287 + 0.0617769i
\(703\) 0.151357 0.00570852
\(704\) 133.336 + 51.3434i 5.02530 + 1.93508i
\(705\) 16.9717 0.639192
\(706\) 52.4259 38.0897i 1.97308 1.43352i
\(707\) 16.5384 + 50.8998i 0.621989 + 1.91429i
\(708\) 0.0111997 0.0344692i 0.000420911 0.00129543i
\(709\) −21.3030 15.4776i −0.800052 0.581272i 0.110877 0.993834i \(-0.464634\pi\)
−0.910929 + 0.412562i \(0.864634\pi\)
\(710\) 92.3377 + 67.0872i 3.46537 + 2.51774i
\(711\) −0.331447 + 1.02009i −0.0124302 + 0.0382563i
\(712\) −19.8754 61.1702i −0.744862 2.29245i
\(713\) 4.57418 3.32333i 0.171304 0.124460i
\(714\) −6.13916 −0.229752
\(715\) −5.03169 7.76593i −0.188175 0.290429i
\(716\) −78.6254 −2.93837
\(717\) −18.5380 + 13.4686i −0.692313 + 0.502995i
\(718\) 25.6707 + 79.0062i 0.958021 + 2.94849i
\(719\) 8.31147 25.5801i 0.309965 0.953976i −0.667812 0.744330i \(-0.732769\pi\)
0.977777 0.209646i \(-0.0672310\pi\)
\(720\) 39.7380 + 28.8713i 1.48095 + 1.07597i
\(721\) −9.20080 6.68477i −0.342656 0.248954i
\(722\) 16.1584 49.7306i 0.601355 1.85078i
\(723\) 3.83560 + 11.8048i 0.142647 + 0.439024i
\(724\) −31.0637 + 22.5691i −1.15447 + 0.838775i
\(725\) −7.53361 −0.279791
\(726\) −26.5597 + 15.2601i −0.985725 + 0.566357i
\(727\) −17.4868 −0.648550 −0.324275 0.945963i \(-0.605120\pi\)
−0.324275 + 0.945963i \(0.605120\pi\)
\(728\) 34.6751 25.1929i 1.28514 0.933712i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) −33.9004 + 104.335i −1.25471 + 3.86160i
\(731\) 1.63356 + 1.18685i 0.0604193 + 0.0438972i
\(732\) 45.9053 + 33.3521i 1.69671 + 1.23273i
\(733\) −14.6925 + 45.2188i −0.542679 + 1.67019i 0.183767 + 0.982970i \(0.441171\pi\)
−0.726446 + 0.687224i \(0.758829\pi\)
\(734\) 7.95049 + 24.4691i 0.293458 + 0.903171i
\(735\) 22.1343 16.0815i 0.816437 0.593176i
\(736\) 198.105 7.30224
\(737\) 7.47570 + 11.5380i 0.275371 + 0.425008i
\(738\) −9.22956 −0.339745
\(739\) 20.3949 14.8178i 0.750239 0.545081i −0.145662 0.989334i \(-0.546531\pi\)
0.895901 + 0.444254i \(0.146531\pi\)
\(740\) 1.59246 + 4.90107i 0.0585398 + 0.180167i
\(741\) 0.145719 0.448476i 0.00535311 0.0164752i
\(742\) 118.454 + 86.0621i 4.34860 + 3.15944i
\(743\) 10.3196 + 7.49763i 0.378589 + 0.275061i 0.760764 0.649029i \(-0.224825\pi\)
−0.382174 + 0.924090i \(0.624825\pi\)
\(744\) −2.59238 + 7.97853i −0.0950413 + 0.292507i
\(745\) 7.37422 + 22.6955i 0.270170 + 0.831499i
\(746\) 21.3024 15.4771i 0.779938 0.566658i
\(747\) 1.76203 0.0644693
\(748\) −9.57806 3.68820i −0.350209 0.134854i
\(749\) 23.3556 0.853394
\(750\) 13.9268 10.1184i 0.508534 0.369472i
\(751\) −9.61804 29.6013i −0.350967 1.08017i −0.958311 0.285727i \(-0.907765\pi\)
0.607344 0.794439i \(-0.292235\pi\)
\(752\) −33.0929 + 101.850i −1.20678 + 3.71407i
\(753\) −4.67644 3.39763i −0.170419 0.123817i
\(754\) 6.09561 + 4.42872i 0.221989 + 0.161285i
\(755\) −10.1536 + 31.2495i −0.369526 + 1.13729i
\(756\) −7.28991 22.4360i −0.265132 0.815991i
\(757\) −6.60370 + 4.79787i −0.240015 + 0.174381i −0.701290 0.712876i \(-0.747392\pi\)
0.461275 + 0.887257i \(0.347392\pi\)
\(758\) −31.7598 −1.15357
\(759\) −14.7263 + 18.1466i −0.534532 + 0.658679i
\(760\) −13.7553 −0.498956
\(761\) −19.6793 + 14.2978i −0.713374 + 0.518296i −0.884260 0.466994i \(-0.845337\pi\)
0.170886 + 0.985291i \(0.445337\pi\)
\(762\) −18.5081 56.9622i −0.670479 2.06352i
\(763\) −0.358794 + 1.10426i −0.0129892 + 0.0399767i
\(764\) −83.0255 60.3215i −3.00376 2.18236i
\(765\) −1.21385 0.881917i −0.0438870 0.0318858i
\(766\) 30.7611 94.6730i 1.11144 3.42067i
\(767\) −0.00194626 0.00598998i −7.02754e−5 0.000216286i
\(768\) −73.8815 + 53.6780i −2.66597 + 1.93694i
\(769\) −15.0974 −0.544427 −0.272214 0.962237i \(-0.587756\pi\)
−0.272214 + 0.962237i \(0.587756\pi\)
\(770\) 102.066 27.2340i 3.67822 0.981445i
\(771\) −15.9866 −0.575745
\(772\) −66.2361 + 48.1233i −2.38389 + 1.73200i
\(773\) −12.7060 39.1051i −0.457004 1.40651i −0.868767 0.495221i \(-0.835087\pi\)
0.411763 0.911291i \(-0.364913\pi\)
\(774\) −3.23100 + 9.94399i −0.116136 + 0.357429i
\(775\) −1.80746 1.31319i −0.0649258 0.0471713i
\(776\) 30.6148 + 22.2429i 1.09901 + 0.798475i
\(777\) 0.406616 1.25144i 0.0145873 0.0448950i
\(778\) 9.44880 + 29.0804i 0.338756 + 1.04258i
\(779\) 1.26443 0.918663i 0.0453029 0.0329145i
\(780\) 16.0552 0.574869
\(781\) 2.60093 48.6532i 0.0930688 1.74095i
\(782\) −10.5521 −0.377343
\(783\) 2.18898 1.59038i 0.0782276 0.0568357i
\(784\) 53.3480 + 164.188i 1.90529 + 5.86387i
\(785\) 8.01084 24.6548i 0.285919 0.879969i
\(786\) 15.4984 + 11.2602i 0.552810 + 0.401640i
\(787\) 12.9819 + 9.43187i 0.462753 + 0.336210i 0.794610 0.607120i \(-0.207675\pi\)
−0.331857 + 0.943330i \(0.607675\pi\)
\(788\) 24.9599 76.8188i 0.889161 2.73655i
\(789\) −1.39842 4.30389i −0.0497851 0.153223i
\(790\) 6.74180 4.89820i 0.239862 0.174270i
\(791\) −2.28127 −0.0811126
\(792\) 1.85106 34.6260i 0.0657746 1.23038i
\(793\) 9.86050 0.350157
\(794\) −19.6365 + 14.2667i −0.696872 + 0.506307i
\(795\) 11.0580 + 34.0330i 0.392186 + 1.20703i
\(796\) 7.97826 24.5545i 0.282782 0.870313i
\(797\) −9.17494 6.66599i −0.324993 0.236121i 0.413310 0.910590i \(-0.364373\pi\)
−0.738303 + 0.674469i \(0.764373\pi\)
\(798\) 4.35513 + 3.16418i 0.154170 + 0.112011i
\(799\) 1.01087 3.11114i 0.0357621 0.110064i
\(800\) −24.1898 74.4486i −0.855239 2.63216i
\(801\) −4.97697 + 3.61598i −0.175853 + 0.127764i
\(802\) −92.9074 −3.28068
\(803\) 45.2478 12.0733i 1.59676 0.426058i
\(804\) −23.8536 −0.841252
\(805\) 65.2029 47.3727i 2.29810 1.66967i
\(806\) 0.690477 + 2.12507i 0.0243210 + 0.0748524i
\(807\) 1.80888 5.56717i 0.0636757 0.195974i
\(808\) −110.423 80.2271i −3.88467 2.82238i
\(809\) −20.7855 15.1015i −0.730778 0.530941i 0.159031 0.987274i \(-0.449163\pi\)
−0.889809 + 0.456332i \(0.849163\pi\)
\(810\) 2.40087 7.38913i 0.0843581 0.259627i
\(811\) 7.34603 + 22.6087i 0.257954 + 0.793901i 0.993233 + 0.116136i \(0.0370510\pi\)
−0.735279 + 0.677764i \(0.762949\pi\)
\(812\) −51.6394 + 37.5182i −1.81219 + 1.31663i
\(813\) −14.0384 −0.492350
\(814\) 1.86799 2.30184i 0.0654730 0.0806794i
\(815\) 63.5141 2.22480
\(816\) 7.65939 5.56487i 0.268132 0.194809i
\(817\) −0.547133 1.68390i −0.0191418 0.0589123i
\(818\) 28.8519 88.7970i 1.00878 3.10472i
\(819\) −3.31659 2.40964i −0.115891 0.0841997i
\(820\) 43.0505 + 31.2780i 1.50339 + 1.09228i
\(821\) 7.09436 21.8342i 0.247595 0.762019i −0.747604 0.664145i \(-0.768796\pi\)
0.995199 0.0978738i \(-0.0312042\pi\)
\(822\) −10.6612 32.8119i −0.371854 1.14445i
\(823\) 7.57934 5.50671i 0.264199 0.191952i −0.447797 0.894135i \(-0.647791\pi\)
0.711996 + 0.702183i \(0.247791\pi\)
\(824\) 29.0041 1.01041
\(825\) 8.61773 + 3.31840i 0.300031 + 0.115532i
\(826\) 0.0719000 0.00250172
\(827\) −20.2809 + 14.7349i −0.705235 + 0.512383i −0.881633 0.471936i \(-0.843555\pi\)
0.176398 + 0.984319i \(0.443555\pi\)
\(828\) −12.5301 38.5636i −0.435450 1.34018i
\(829\) 2.08322 6.41150i 0.0723533 0.222681i −0.908340 0.418232i \(-0.862650\pi\)
0.980693 + 0.195552i \(0.0626498\pi\)
\(830\) −11.0754 8.04672i −0.384431 0.279306i
\(831\) −4.57455 3.32361i −0.158689 0.115295i
\(832\) −13.3124 + 40.9715i −0.461526 + 1.42043i
\(833\) −1.62959 5.01537i −0.0564620 0.173772i
\(834\) −39.4246 + 28.6436i −1.36516 + 0.991847i
\(835\) −19.6953 −0.681584
\(836\) 4.89376 + 7.55304i 0.169254 + 0.261227i
\(837\) 0.802399 0.0277350
\(838\) 18.6107 13.5215i 0.642896 0.467092i
\(839\) 13.8118 + 42.5085i 0.476838 + 1.46756i 0.843463 + 0.537187i \(0.180513\pi\)
−0.366625 + 0.930369i \(0.619487\pi\)
\(840\) −36.9533 + 113.730i −1.27501 + 3.92407i
\(841\) 17.5387 + 12.7426i 0.604784 + 0.439401i
\(842\) −16.0620 11.6697i −0.553533 0.402165i
\(843\) −6.45427 + 19.8642i −0.222297 + 0.684159i
\(844\) 14.9694 + 46.0712i 0.515269 + 1.58584i
\(845\) 2.25719 1.63994i 0.0776497 0.0564158i
\(846\) 16.9391 0.582380
\(847\) −33.4487 30.2445i −1.14931 1.03921i
\(848\) −225.798 −7.75395
\(849\) −16.0717 + 11.6767i −0.551578 + 0.400745i
\(850\) 1.28848 + 3.96553i 0.0441944 + 0.136017i
\(851\) 0.698901 2.15100i 0.0239580 0.0737352i
\(852\) 68.3909 + 49.6889i 2.34303 + 1.70231i
\(853\) −17.3639 12.6156i −0.594528 0.431950i 0.249405 0.968399i \(-0.419765\pi\)
−0.843932 + 0.536450i \(0.819765\pi\)
\(854\) −34.7850 + 107.057i −1.19032 + 3.66342i
\(855\) 0.406561 + 1.25127i 0.0139041 + 0.0427924i
\(856\) −48.1881 + 35.0107i −1.64704 + 1.19664i
\(857\) −8.46288 −0.289087 −0.144543 0.989498i \(-0.546171\pi\)
−0.144543 + 0.989498i \(0.546171\pi\)
\(858\) −5.02204 7.75103i −0.171449 0.264616i
\(859\) −32.1582 −1.09722 −0.548611 0.836078i \(-0.684843\pi\)
−0.548611 + 0.836078i \(0.684843\pi\)
\(860\) 48.7699 35.4334i 1.66304 1.20827i
\(861\) −4.19876 12.9224i −0.143093 0.440396i
\(862\) 21.5226 66.2399i 0.733064 2.25614i
\(863\) −13.1749 9.57215i −0.448480 0.325840i 0.340515 0.940239i \(-0.389398\pi\)
−0.788995 + 0.614399i \(0.789398\pi\)
\(864\) 22.7451 + 16.5253i 0.773805 + 0.562202i
\(865\) 6.87153 21.1484i 0.233639 0.719066i
\(866\) 11.2910 + 34.7500i 0.383683 + 1.18085i
\(867\) 13.5193 9.82236i 0.459140 0.333585i
\(868\) −18.9291 −0.642496
\(869\) −3.31974 1.27832i −0.112615 0.0433641i
\(870\) −21.0218 −0.712706
\(871\) −3.35356 + 2.43650i −0.113631 + 0.0825577i
\(872\) −0.915035 2.81619i −0.0309870 0.0953681i
\(873\) 1.11848 3.44234i 0.0378550 0.116506i
\(874\) 7.48568 + 5.43867i 0.253207 + 0.183966i
\(875\) 20.5026 + 14.8960i 0.693113 + 0.503576i
\(876\) −25.1087 + 77.2766i −0.848344 + 2.61093i
\(877\) 4.20103 + 12.9295i 0.141859 + 0.436597i 0.996594 0.0824682i \(-0.0262803\pi\)
−0.854735 + 0.519065i \(0.826280\pi\)
\(878\) −52.4177 + 38.0837i −1.76901 + 1.28526i
\(879\) 29.7117 1.00215
\(880\) −102.654 + 126.496i −3.46048 + 4.26419i
\(881\) −27.4177 −0.923725 −0.461862 0.886952i \(-0.652819\pi\)
−0.461862 + 0.886952i \(0.652819\pi\)
\(882\) 22.0918 16.0507i 0.743871 0.540454i
\(883\) 6.52446 + 20.0802i 0.219566 + 0.675753i 0.998798 + 0.0490181i \(0.0156092\pi\)
−0.779232 + 0.626735i \(0.784391\pi\)
\(884\) 0.956284 2.94314i 0.0321633 0.0989885i
\(885\) 0.0142163 + 0.0103288i 0.000477876 + 0.000347197i
\(886\) 73.9219 + 53.7074i 2.48345 + 1.80434i
\(887\) −6.19632 + 19.0703i −0.208052 + 0.640318i 0.791522 + 0.611140i \(0.209289\pi\)
−0.999574 + 0.0291780i \(0.990711\pi\)
\(888\) 1.03700 + 3.19154i 0.0347993 + 0.107101i
\(889\) 71.3339 51.8271i 2.39246 1.73822i
\(890\) 47.7963 1.60213
\(891\) −3.20451 + 0.855048i −0.107355 + 0.0286452i
\(892\) −89.0754 −2.98247
\(893\) −2.32063 + 1.68604i −0.0776569 + 0.0564210i
\(894\) 7.36007 + 22.6520i 0.246157 + 0.757595i
\(895\) 11.7801 36.2555i 0.393766 1.21189i
\(896\) −211.383 153.579i −7.06182 5.13071i
\(897\) −5.70062 4.14175i −0.190338 0.138289i
\(898\) −15.3971 + 47.3874i −0.513808 + 1.58134i
\(899\) −0.670898 2.06481i −0.0223757 0.0688653i
\(900\) −12.9623 + 9.41769i −0.432078 + 0.313923i
\(901\) 6.89734 0.229784
\(902\) 1.63409 30.5673i 0.0544092 1.01778i
\(903\) −15.3926 −0.512234
\(904\) 4.70680 3.41969i 0.156546 0.113737i
\(905\) −5.75284 17.7054i −0.191231 0.588549i
\(906\) −10.1341 + 31.1895i −0.336683 + 1.03620i
\(907\) −12.1177 8.80400i −0.402360 0.292332i 0.368141 0.929770i \(-0.379994\pi\)
−0.770502 + 0.637438i \(0.779994\pi\)
\(908\) −24.8131 18.0278i −0.823452 0.598273i
\(909\) −4.03421 + 12.4160i −0.133806 + 0.411813i
\(910\) 9.84245 + 30.2919i 0.326274 + 1.00417i
\(911\) −30.3517 + 22.0518i −1.00560 + 0.730609i −0.963281 0.268495i \(-0.913474\pi\)
−0.0423165 + 0.999104i \(0.513474\pi\)
\(912\) −8.30177 −0.274899
\(913\) −0.311967 + 5.83566i −0.0103246 + 0.193132i
\(914\) 60.7171 2.00834
\(915\) −22.2570 + 16.1707i −0.735795 + 0.534586i
\(916\) 32.9960 + 101.551i 1.09022 + 3.35534i
\(917\) −8.71504 + 26.8221i −0.287796 + 0.885745i
\(918\) −1.21153 0.880225i −0.0399863 0.0290517i
\(919\) −20.9454 15.2177i −0.690924 0.501986i 0.186039 0.982542i \(-0.440435\pi\)
−0.876964 + 0.480556i \(0.840435\pi\)
\(920\) −63.5161 + 195.482i −2.09406 + 6.44486i
\(921\) −2.99840 9.22812i −0.0988006 0.304077i
\(922\) 34.7152 25.2221i 1.14328 0.830645i
\(923\) 14.6904 0.483541
\(924\) 75.5965 20.1711i 2.48694 0.663582i
\(925\) −0.893693 −0.0293844
\(926\) 70.4226 51.1650i 2.31423 1.68139i
\(927\) −0.857268 2.63840i −0.0281564 0.0866564i
\(928\) 23.5070 72.3470i 0.771654 2.37491i
\(929\) −39.7104 28.8513i −1.30286 0.946581i −0.302878 0.953029i \(-0.597947\pi\)
−0.999979 + 0.00644820i \(0.997947\pi\)
\(930\) −5.04353 3.66434i −0.165384 0.120159i
\(931\) −1.42894 + 4.39782i −0.0468315 + 0.144133i
\(932\) 23.3790 + 71.9531i 0.765804 + 2.35690i
\(933\) −2.02785 + 1.47332i −0.0663890 + 0.0482344i
\(934\) 36.6816 1.20026
\(935\) 3.13573 3.86402i 0.102549 0.126367i
\(936\) 10.4550 0.341734
\(937\) 28.4120 20.6425i 0.928179 0.674361i −0.0173675 0.999849i \(-0.505529\pi\)
0.945546 + 0.325488i \(0.105529\pi\)
\(938\) −14.6231 45.0054i −0.477463 1.46948i
\(939\) 9.54455 29.3751i 0.311475 0.958621i
\(940\) −79.0113 57.4051i −2.57707 1.87235i
\(941\) 25.7924 + 18.7393i 0.840809 + 0.610884i 0.922597 0.385766i \(-0.126063\pi\)
−0.0817873 + 0.996650i \(0.526063\pi\)
\(942\) 7.99547 24.6075i 0.260506 0.801757i
\(943\) −7.21691 22.2114i −0.235015 0.723302i
\(944\) −0.0897045 + 0.0651741i −0.00291963 + 0.00212124i
\(945\) 11.4379 0.372073
\(946\) −32.3614 12.4613i −1.05216 0.405152i
\(947\) 19.2891 0.626810 0.313405 0.949620i \(-0.398530\pi\)
0.313405 + 0.949620i \(0.398530\pi\)
\(948\) 4.99338 3.62790i 0.162178 0.117829i
\(949\) 4.36333 + 13.4289i 0.141640 + 0.435922i
\(950\) 1.12983 3.47725i 0.0366564 0.112817i
\(951\) −2.33944 1.69970i −0.0758615 0.0551166i
\(952\) 18.6473 + 13.5481i 0.604363 + 0.439095i
\(953\) −8.18792 + 25.1998i −0.265233 + 0.816303i 0.726407 + 0.687265i \(0.241189\pi\)
−0.991640 + 0.129038i \(0.958811\pi\)
\(954\) 11.0368 + 33.9677i 0.357328 + 1.09974i
\(955\) 40.2546 29.2467i 1.30261 0.946401i
\(956\) 131.859 4.26463
\(957\) 4.87963 + 7.53124i 0.157736 + 0.243450i
\(958\) −34.9575 −1.12943
\(959\) 41.0905 29.8540i 1.32688 0.964035i
\(960\) −37.1422 114.312i −1.19876 3.68941i
\(961\) −9.38057 + 28.8704i −0.302599 + 0.931304i
\(962\) 0.723107 + 0.525368i 0.0233139 + 0.0169385i
\(963\) 4.60908 + 3.34869i 0.148525 + 0.107910i
\(964\) 22.0719 67.9302i 0.710887 2.18789i
\(965\) −12.2666 37.7527i −0.394875 1.21530i
\(966\) 65.0778 47.2818i 2.09384 1.52127i
\(967\) −30.5524 −0.982500 −0.491250 0.871019i \(-0.663460\pi\)
−0.491250 + 0.871019i \(0.663460\pi\)
\(968\) 114.350 + 12.2610i 3.67535 + 0.394085i
\(969\) 0.253590 0.00814647
\(970\) −22.7506 + 16.5292i −0.730476 + 0.530722i
\(971\) −15.0123 46.2031i −0.481767 1.48273i −0.836609 0.547800i \(-0.815465\pi\)
0.354842 0.934926i \(-0.384535\pi\)
\(972\) 1.77823 5.47283i 0.0570368 0.175541i
\(973\) −58.0396 42.1683i −1.86066 1.35185i
\(974\) 17.7972 + 12.9304i 0.570260 + 0.414318i
\(975\) −0.860404 + 2.64805i −0.0275550 + 0.0848055i
\(976\) −53.6438 165.099i −1.71710 5.28468i
\(977\) −11.9217 + 8.66160i −0.381408 + 0.277109i −0.761926 0.647665i \(-0.775746\pi\)
0.380518 + 0.924774i \(0.375746\pi\)
\(978\) 63.3923 2.02706
\(979\) −11.0946 17.1234i −0.354584 0.547266i
\(980\) −157.440 −5.02923
\(981\) −0.229133 + 0.166475i −0.00731564 + 0.00531512i
\(982\) 1.76272 + 5.42508i 0.0562505 + 0.173121i
\(983\) 12.5558 38.6427i 0.400467 1.23251i −0.524155 0.851623i \(-0.675619\pi\)
0.924622 0.380887i \(-0.124381\pi\)
\(984\) 28.0342 + 20.3680i 0.893698 + 0.649309i
\(985\) 31.6828 + 23.0189i 1.00950 + 0.733442i
\(986\) −1.25211 + 3.85358i −0.0398751 + 0.122723i
\(987\) 7.70605 + 23.7168i 0.245286 + 0.754913i
\(988\) −2.19531 + 1.59499i −0.0698422 + 0.0507433i
\(989\) −26.4571 −0.841288
\(990\) 24.0469 + 9.25968i 0.764262 + 0.294292i
\(991\) 55.7863 1.77211 0.886056 0.463579i \(-0.153435\pi\)
0.886056 + 0.463579i \(0.153435\pi\)
\(992\) 18.2507 13.2599i 0.579459 0.421002i
\(993\) −4.16474 12.8178i −0.132164 0.406760i
\(994\) −51.8235 + 159.496i −1.64374 + 5.05892i
\(995\) 10.1272 + 7.35781i 0.321053 + 0.233258i
\(996\) −8.20308 5.95989i −0.259925 0.188846i
\(997\) −5.51651 + 16.9781i −0.174709 + 0.537700i −0.999620 0.0275627i \(-0.991225\pi\)
0.824911 + 0.565263i \(0.191225\pi\)
\(998\) 22.1501 + 68.1711i 0.701150 + 2.15792i
\(999\) 0.259673 0.188663i 0.00821568 0.00596904i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 429.2.n.d.157.9 36
11.2 odd 10 4719.2.a.br.1.18 18
11.4 even 5 inner 429.2.n.d.235.9 yes 36
11.9 even 5 4719.2.a.bq.1.1 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.n.d.157.9 36 1.1 even 1 trivial
429.2.n.d.235.9 yes 36 11.4 even 5 inner
4719.2.a.bq.1.1 18 11.9 even 5
4719.2.a.br.1.18 18 11.2 odd 10